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Currently 22-23 magnitude could be the limit to make a spectrum for ground based 10m class telescopes, 21-22 magnitude may be easy for them.
4m class telescopes could possibly handle 20 magnitude, I am not sure.
2m could be appropriate for stars brighter than 16magnitude generally.

What about the infrared bands: J H K W1 W2 respectively? Are there any empirical values or references?

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  • $\begingroup$ A spectrum with what resolution and with what signal to noise? $\endgroup$ – ProfRob Mar 7 '16 at 21:38
  • $\begingroup$ and of what kind of source? $\endgroup$ – ProfRob May 13 '20 at 14:41
  • $\begingroup$ Many observatories have exposure calculators for their telescope/instrument combinations. These are usually found via the astronomer section especially related to making a submission for observing time. Most are an on-line interface rather than a code download. $\endgroup$ – TazAstroSpacial Sep 3 '20 at 3:29
  • $\begingroup$ As for a relationship. If comparing like for like instruments (band, resolution) on different sized telescopes the first factor is just telescope primary area. Double area double photons half exposure time for same magnitude limit, roughly increase by 1 magnitude (2.51 factor for 1 magnitude). But at faint limit background is important so need for 1 mag more need 2.51 times more photons above background. ... So in principle you could calculate it yourself but play with exposure calculators it's far easier than re-inventing that wheel. $\endgroup$ – TazAstroSpacial Sep 3 '20 at 3:36

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